相关论文: Boundary controllability of a one-dimensional phas…

In this paper, we prove the null controllability of a one-dimensional fourth-order degenerate parabolic equation with a singular potential. Here, we analyze cases where boundary control conditions are applied at the left endpoint. We…

In this paper, we continue the study of some controllability issues for the forward stochastic parabolic equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…

In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on a phase-field model of grain boundary motion, proposed in…

We consider linear one-dimensional parabolic equations with space dependent coefficients that are only measurable and that may be degenerate or singular.Considering generalized Robin-Neumann boundary conditions at both extremities, we prove…

In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs $((u_{\varepsilon}, h_{\varepsilon}))_{\varepsilon >0}$ solving…

In this article, we study the boundary null-controllability properties of the one-dimensional linearized (around $(Q_0,V_0)$ with constants $Q_0>0, V_0>0$) compressible Navier-Stokes equations in the interval $(0,1)$ when a control function…

This paper deals with the problem of internal null-controllability of a heat equation posed on a bounded domain with Dirichlet boundary conditions and perturbed by a semilinear nonlocal term. We prove the small-time local…

In this paper, we study the controllability of a Schr\"odinger equation with mixed boundary conditions on disjoint subsets of the boundary: dynamic boundary condition of Wentzell type, and Dirichlet boundary condition. The main result of…

We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null…

We consider the 1D nonlinear Schr\"odinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in…

We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…

This paper deals with the analysis of the internal control with constraint of positive kind of a parabolic PDE with nonlinear diffusion when the time horizon is large enough. The minimal controllability time will be strictly positive. We…

This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…

We study the null controllability for a degenerate/singular wave equation with drift in non divergence form. In particular, considering a control localized on the non degenerate boundary point, we provide some conditions for the boundary…

This article is dedicated to improve the controllability results obtained by Cerpa et al. in Commun. Contemp. Math 13 (2011) and by Micu et al. in Commun. Contemp. Math 11 (5) (2009) for a nonlinear coupled system of two Korteweg-de Vries…

In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…

In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a…

We study the existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a Hilbert space. The results are obtained by using semigroup theory, fractional calculus, and Schauder's fixed…

We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.

This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…